Questions and Answers of Principles Communications Systems

Capacitors tend to be more expensive as their capacitance and maximum voltage Vmax increase. The voltage Vmax is limited by the field strength at which the dielectric breaks down, EBD. Which of these
An antenna with a temperature of 300° K is fed into a receiver with a total gain of 80 dB, Te = 1500° K, and a bandwidth of 3 MHz.(a) Find the available noise power at the output of the
Given a cascade of a preamplifier, mixer, and amplifier with the specifications shown in Table A.2, (a) Find the gain of the preamplifier such that the overall noise figure of the cascade is 5 dB or
An attenuator with loss L» 1 is followed by an amplifier with noise figure F and gain Ga = 1 /L.(a) Find the noise figure of the cascade at tempera true T0.(b) Consider the cascade of two identical
A source with equivalent noise temperature Ts = 1000? K is followed by a cascade of three amplifiers having the specifications shown in Table A. 1. Assume a band width of 50 kHz. (a) Find the noise
Obtain an expression for F and Te for the two-port resistive matching network shown in Figure A.10, assuming a source at T0 = 290? K. R1 R2
Assuming a bandwidth of 2 MHz, find the rms noise voltage across the output terminals of the circuit shown in Figure A.9 if it is at a temperature of 400?K. 5 k2 50 k2 Vrms 10kΩ 20 kΩ 5kΩ
Referring to the circuit of Figure A.8, consider RL to be a load resistance, and find it in terms of R1, R2, and R3 so that the maximum available noise power available from R1, R2, and R3 is
Consider the circuit shown in Figure A.8. (a) Obtain an expression for the mean-square noise voltage appearing across R3. (b) If R1 = 2000 ?, R2 = RL = 300 ?, and R3 = 500 ?, find the mean-square
Given a junction diode with reverse saturation current Is = 15 μA.(a) At room temperature (290◦K), find V such that I > 20Is, thus allowing (A.16) to be approximated by (A.17). Find the rms
(a) Using the results of Problem D.1, derive Equation (D.28) with |δ̅f̅| = fd.(b) Compare Equations (D.28) and (D.23) for a square wave-modulated FM signal with deviation fd. by letting
A true rms voltmeter (assumed noiseless) with an effective noise bandwidth of 30 MHz is used to measure the noise voltage produced by the following devices. Calculate the meter reading in each
Consider a signal-plus-noise process of the form z(t) = A cos 2?(f0 + fd)t + n(t)? ? ? ? ? ? ? ? ? ? ? ?? ? ? ? ? ? ? ??(D.29) where n(t) is given by n(t) = nc(t) cos 2?f0t ? ns(t) sin 2?f0t? ? ? ? ?
A communications system operates with a message signal bandwidth of 10 kHz and a transmission bandwidth of 250 kHz. What is the bandwidth expansion factor? Assuming a pre-detection SNR of 20 dB and
A communications system uses feedback to increase reliability. The system is modeled as a binary erasure channel with an erasure probability of 0.01. Determine the average number of transmissions
A convolutional code has a constraint span of 5. Assuming that data symbols are input to the coder one bit at a time, how many states does it take to define the state diagram of the coder?
A (7,4) single error-correcting code has the source symbols in positions 1, 2, 6, and 7. Write the generator matrix for this code.
Consider a (5,4) code. What kind of code is this? How many errors per code word can be corrected? How many errors per code word can be detected? Give the generator matrix of this code.
Give the transmitted code words of a rate 1/7 repetition code. What is the Hamming distance between the code words? How many errors per code word can be corrected?
A communications system operates in an AWGN channel with a signal-to-noise ratio of 25 dB. The channel bandwidth is 15 kHz. Determine the channel capacity in bps.
The symbol probabilities of a binary source are 0.4 and 0.6. Determine the entropy of the fifth-order source extension.
A binary symmetric channel has an error probability of 0.001. Determine the channel capacity.
A binary symmetric channel has an error probability of 0.001. Write the channel transition probability matrix. Assuming that the input probabilities are 0.3 and 0.7, determine the output
A communication system consists of two binary symmetric channels in cascade. The first BSC has an error probability of 0.03 and the second BSC has an error probability of 0.07. Determine the error
A source has three outputs with probabilities 1/6,1/2, and 1/3. Determine the entropy of the source. Give the source probabilities that yield the maximum entropy for a source with three outputs.
(a) A source outputs 73 equally likely messages. Determine the information, in bits, associated with each message. (b) Repeat assuming that there are 37 equally likely messages.
A message occurs with a probability of 0.8. Determine the information associated with the message in bits, nats, and hartleys.
What is an efficient estimate?
What is the usefulness of the Cramer-Rao inequality?
Explain the principle of using a sufficient statistic in making a decision or estimating a parameter.
Name three characteristics of maximum likelihood estimators in the limit of large sample sizes.
Contrast the Bayes and maximum-likelihood estimation procedures.
Why use the signal-space approach for analysis of digital communication systems?
What does the Gram-Schmidt procedure accomplish?
What ingredients go into defining a signal space?
(a) What is the decision strategy of the Neyman Pearson detector?(b) How is it implemented?
Name the three things that must be known in order to design a Bayes receiver.
Tell what the abbreviations 1G, 2G, 3G, and 4G mean and the approximate dates of their implementation.
Tell what the abbreviation MIMO stands for and what advantages accrue from its employment.
What are two gross characterizations of the type of multi path typically found in cellular radio systems.
While free-space propagation of electromagnetic waves is typically characterized by an inverse square-law decrease in power density with distance from the source, what is the range of power law
An OFDM system is designed to combat multi path having delay spread τm. QPSK is used as the data modulation. If the delay spread doubles, tell how the system should be redesigned in order to provide
What is a major use of OFDM? What advantages does it provide?
For a serial-search code acquisition system, what determines the amount of search time required to acquire the code? If the uncertainty of the code epoch doubles from that assumed in the design of
The JSR un-expectantly increases in a spread spectrum system by 10 dB. What means can be used to combat this?
List three reasons for using spread spectrum.
Pseudo-noise sequences can be generated simply of almost any length. Name some disadvantages that prevent them from being universally used.
Compare M-ary PSK and QAM in terms of power and bandwidth efficiency.
What are three types of synchronization required in a communication system?
(a) Compare M-ary PSK and DPSK with regard to power and bandwidth efficiency.(b) Compare M-ary coherent FSK and non-coherent FSK with regard to power and bandwidth efficiency.
Compare QPSK, OQPSK, and MSK in as many ways you can think of.
What two sources of noise affect the convergence of a tap weight adjustment algorithm for an equalizer?
What is the minimum number of taps required to equalize a channel, which produces two multi path components plus the main path? That is, the channel input-output relationship is given by y(t) =
A two-path channel consists of a direct path and one delayed path. The delayed path has a delay of 5 microseconds. The channel can be considered flat fading if the phase shift induced by the delayed
What might be an effective communication scheme in a flat-fading channel if one could determine when the channel goes into a deep fade? What is the downside of this scheme? (What would happen if the
Referring to Figure 9.24, where f3 / R = 0.5, what behavior would you expect the curves to exhibit if f3 / R = 1? Why? Figure 9.24 f3/R = 0.5 %3D 3 3 2.5 2.5 HAf): no. poles = 1 HAf): no. poles = 2
Antipodal base band PAM is used to transmit data through a low pass channel of bandwidth 10 kHz with AWGN background. Give the required value of M, to the next higher power of 2, for the following
The input signal to a matched filter is given by The noise is white with signal-sided power spectral density N0 = 10-1 W/Hz. What is the peak signal-squared-to-mean-square-noise ratio at its output?
(a) Rank the following binary modulation schemes in terms of Eb / N0 required to give PE = 10-6 from best to worst (the lowest required Eb / N0 is the best system): PSK; coherent FSK; DPSK; coherent
Consider PSK with 10% of the transmitted signal power in a carrier component.(a) What is the value of m for the transmitted signal?(b) What is the change in phase in degrees each time the data
Taking the required channel bandwidth to be the first null of the rectangular pulse representing a 1 or 0 (plus for 1 and minus for 0), give bandwidths for the following data rates for a base band
Given that Q (√2z) = 10-6 for z = 11.31 find the following:(a) The signal amplitude (assume rectangular pulses) for antipodal base band signaling that gives PE = 10-6 in a channel with N0 =
A compressor has the amplitude compression characteristic of a first-order Butter worth high-pass filter. Assuming that the input signal has negligible content for f ≤ f1 where f1 << f3,
The performance of a PCM system is limited by quantizing error. What word length is required to ensure an output SNR of at least 35 dB?
An FM system operates with the same parameters as given in the preceding drill problem except that the deviation ratio is 5. Determine the channel noise PSD that results in a post detection SNR of 30
A PM system operates with a transmitter power of 10 kW and a message signal bandwidth of 10 kHz. The phase modulation constant is π radians per unit input. The normalized message signal has a
An SSB system operates at a signal-to-noise ratio of 20 dB. The demodulation phase-error standard deviation is 5 degrees. Determine the mean-square error between the original message signal and the
A signal in a simple system is defined by 5 cos [2π(6)t]. This signal is subjected to additive single tone interference defined by 0.2 sin [2π(8)t]. Determine the signal-to-interference ratio.
The input to a receiver has a signal component having the PSD SS(f) = 5Λ(f/7). The noise component is (10-4) II(f/20). Determine the SNR in dB.
A 10,000 ohm resistor operates at a temperature of 290 K. Determine the variance of the noise generated in a bandwidth of 1,000,000 Hz.
A band limited signal consists of a steady sinusoidal component of power 10 Wand a narrow band Gaussian component centered on the steady component of power 5 W. Find the following:(a) The steady
A filter has frequency response function H (f) = Λ(f / 2). What is its noise- equivalent bandwidth?
A band pass random process has power spectral density S(f) = II (f - 10/4) + II (f + 10/4).(a) Find its auto correlation function.(b) It is to be represented in in phase quadrature form; that
A filter with frequency response function H(f) = (1 + j2πf)-1 is driven by a white-noise process with double-sided power spectral density of 1 W/Hz.(a) What is the cross-power spectral density
For each case given below, tell whether the given function can be a satisfactory auto correlation function. If it is not satisfactory, give the reason(s).(a) Ra (τ) = II (τ/τ0) where τ0 is a
White Gaussian noise of double-sided power spectral density 1 W/Hz is passed through a filter with frequency response function H(f) = (1 +j2πf)-1.(a) What is the power spectral density, SY(f),
A random process is defined by the sample functions Xi. (t) = Ait + Bi, where t is time in seconds, the As are in dependent random variables for each i, which are Gaussian with 0 means and unit
The probability of error on a single transmission in a digital communication system is PE = 10-3. (a) What is the probability of 0 errors in 100 transmissions? (b) 1 error in 100?(c) 2
A fair coin is tossed 100 times. According to the Laplace approximation, what is the probability that exactly (a) 50 heads are obtained? (b) 51 heads? (c) 52 heads? (d) Is the
A random variable is defined as the sum of ten independent random variables, which are all uniformly distributed in [-0.5, 0.5].(a) According to the central-limit theorem, write down an approximate
The characteristic function of a random variable, X, is MX (jv) = (1 + v2)-1.Find the following:(a) The mean of X;(b) The variance of X;(c) The pdf of X;
Let a random variable Z be defined in terms of three independent random variables as Z = 2X1 + 4X2 + 3X3, where the means of X1, X2, and X3 are -1, 5, and -2, respectively, and their respective
A random variable Z is defined as Z = X + Y where X and Y are Gaussian with the following statistics:1. E[X] = 2, E[Y] = -32. σX = 2, σY = 3, 3. μXY = 0.5
(a) What is the probability of getting two or fewer heads in tossing a fair coin 10 times?(b) What is the probability of getting exactly five heads in tossing a fair coin 10 times?
Given a joint pdf defined as Find the following:(a) fX (x); (b) fY (y);? (c) E[X], E[Y], E[X2], E[Y2], ?2X, ?2Y, (d) E[XY]; (e) uXY. 1, 0 < x < 1, 0
Given a pdf of the form fX(x) = A exp(-αx) u(x - 1), where u(x) is the unit step and A and α are positive constants, do the following:(a) Give the relationship between A and α.(b) Find
(a) What is the probability drawing an ace from a 52-card deck with a single draw?(b) What is the probability drawing the ace of spades from a 52-card deck with a single draw?(c) What is the
Referring to Drill Problem 6.3, find the following:(a) P(A|B);(b) P(B|A);(c) P(A|C);(d) P(C|A);(e) P(B|C);(f) P(C|B);Data From Problem 6.3In tossing a single six-sided fair die, event A = {1 or 3},
Referring to Drill Problem 6.2, find the following:(a) P(A|B);(b) P(B|A);Data From Problem 6.2In tossing a six-sided fair die, we define event A = {2 or 4 or 6} and event B = {1 or 3 or 5 or 6}.
In tossing a single six-sided fair die, event A = {1 or 3}, event B = {2 or 3 or 4}, and event C = {4 or 5 or 6}. Find the following probabilities:(a) P(A);(b) P(B);(c) P(C);(d) P (A ∪ B);(e) P (A
In tossing a six-sided fair die, we define event A = {2 or 4 or 6} and event B = {1 or 3 or 5 or 6}.Using equal likelihood and the axioms of probability, find the following:(a) P(A);(b) P(B);(c) P(A
A fair coin and a fair die (six sides) are tossed simultaneously with neither affecting the outcome of the other. Give probabilities for the following events using the principle of equal
Give advantages and disadvantages of the carrier modulation methods illustrated in Figure 5.19. Figure 5.19 Data ASK PSK FSK
Judging from the results of Figures 5.16. and 5.18, which method for generating a spectral component at the data clock frequency generates a higher-power one: the squarer or the delay-and-multiply
Choose the correct adjective: A narrower bandwidth channel implies (more) (less) amplitude jitter.
Choose the correct adjective: A wider bandwidth channel implies (more) (less) timing jitter.
How many total samples of the incoming pulse are required to force the following number of zeros on either side of the middle sample for a zero-forcing equalizer?(a) 1;(b) 3;(c) 4;(d) 7;(e) 8;(f) 10.
For the data sequence of Problem 5.3 provide waveform sketches for:(a) Unipolar RZ;(b) Polar RZ;(c) Bipolar RZ.Data From Problem 5.3(a) Given the random binary data sequence 0 1 1 0 0
Which of the following pulse spectra have inverse Fourier transforms with the zero-ISI property?(a) P1 (f) = II (Tf) where T is the pulse duration;(b) P2 (f) = Λ (Tf / 2);(c) P3 (f) =
What is meant by a pulse having the zero-ISI property? What must be true of the pulse spectrum in order that it have this property?

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